TSTP Solution File: SET185+3 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Mar 25 14:31:24 EDT 2024
% Result : Theorem 0.67s 0.87s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : SET185+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.10 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Wed Mar 20 21:52:40 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.67/0.87 % SZS status Theorem for theBenchmark
% 0.67/0.87 % SZS output start Proof for theBenchmark
% 0.67/0.87
% 0.67/0.87 % Formula: union_defn ( axiom ) converted to clauses:
% 0.67/0.87 cnf(union_defn-1, axiom, ( ~member(_u3, union(_u7, _u5)) | member(_u3, _u7) | member(_u3, _u5) )).
% 0.67/0.87 cnf(union_defn-2, axiom, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u8) )).
% 0.67/0.87 cnf(union_defn-3, axiom, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u6) )).
% 0.67/0.87
% 0.67/0.87 % Formula: subset_defn ( axiom ) converted to clauses:
% 0.67/0.87 cnf(subset_defn-1, axiom, ( ~subset(_u15, _u13) | ~member(_u9, _u15) | member(_u9, _u13) )).
% 0.67/0.87 cnf(subset_defn-2, axiom, ( subset(_u16, _u14) | member(skolem1(_u16, _u14), _u16) )).
% 0.67/0.87 cnf(subset_defn-3, axiom, ( subset(_u16, _u14) | ~member(skolem1(_u16, _u14), _u14) )).
% 0.67/0.87
% 0.67/0.87 % Formula: equal_defn ( axiom ) converted to clauses:
% 0.67/0.87 cnf(equal_defn-1, axiom, ( ( _u21 != _u19) | subset(_u21, _u19) )).
% 0.67/0.87 cnf(equal_defn-2, axiom, ( ( _u21 != _u19) | subset(_u19, _u21) )).
% 0.67/0.87 cnf(equal_defn-3, axiom, ( ~subset(_u22, _u20) | ~subset(_u20, _u22) | ( _u22 = _u20) )).
% 0.67/0.87
% 0.67/0.87 % Formula: commutativity_of_union ( axiom ) converted to clauses:
% 0.67/0.87 cnf(commutativity_of_union-1, axiom, ( ( union(_u24, _u23) = union(_u23, _u24)) )).
% 0.67/0.87
% 0.67/0.87 % Formula: reflexivity_of_subset ( axiom ) converted to clauses:
% 0.67/0.87 cnf(reflexivity_of_subset-1, axiom, ( subset(_u25, _u25) )).
% 0.67/0.87
% 0.67/0.87 % Formula: equal_member_defn ( axiom ) converted to clauses:
% 0.67/0.87 cnf(equal_member_defn-1, axiom, ( ( _u36 != _u34) | ~member(_u30, _u36) | member(_u30, _u34) )).
% 0.67/0.87 cnf(equal_member_defn-2, axiom, ( ( _u36 != _u34) | ~member(_u31, _u34) | member(_u31, _u36) )).
% 0.67/0.87 cnf(equal_member_defn-3, axiom, ( ( _u37 = _u35) | member(skolem2(_u37, _u35), _u37) | member(skolem3(_u37, _u35), _u35) )).
% 0.67/0.87 cnf(equal_member_defn-4, axiom, ( ( _u37 = _u35) | member(skolem2(_u37, _u35), _u37) | ~member(skolem3(_u37, _u35), _u37) )).
% 0.67/0.87 cnf(equal_member_defn-5, axiom, ( ( _u37 = _u35) | ~member(skolem2(_u37, _u35), _u35) | member(skolem3(_u37, _u35), _u35) )).
% 0.67/0.87 cnf(equal_member_defn-6, axiom, ( ( _u37 = _u35) | ~member(skolem2(_u37, _u35), _u35) | ~member(skolem3(_u37, _u35), _u37) )).
% 0.67/0.87
% 0.67/0.87 % Formula: prove_subset_union ( conjecture ) (definitionally) converted to clauses:
% 0.67/0.87 cnf(prove_subset_union-1, negated_conjecture, ( subset(skolem4, skolem5) )).
% 0.67/0.87 cnf(prove_subset_union-2, negated_conjecture, ( ( union(skolem4, skolem5) != skolem5) )).
% 0.67/0.87
% 0.67/0.87 % Problem matrix:
% 0.67/0.87 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 0.67/0.87 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 0.67/0.87 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 0.67/0.87 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( union(__eqx_0, __eqx_1) = union(__eqy_0, __eqy_1)) )).
% 0.67/0.87 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 0.67/0.87 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 0.67/0.87 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 0.67/0.87 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 0.67/0.87 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 0.67/0.87 cnf(matrix-9, plain, ( ~member(_u3, union(_u7, _u5)) | member(_u3, _u7) | member(_u3, _u5) )).
% 0.67/0.87 cnf(matrix-10, plain, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u8) )).
% 0.67/0.87 cnf(matrix-11, plain, ( member(_u4, union(_u8, _u6)) | ~member(_u4, _u6) )).
% 0.67/0.87 cnf(matrix-12, plain, ( ~subset(_u15, _u13) | ~member(_u9, _u15) | member(_u9, _u13) )).
% 0.67/0.87 cnf(matrix-13, plain, ( subset(_u16, _u14) | member(skolem1(_u16, _u14), _u16) )).
% 0.67/0.87 cnf(matrix-14, plain, ( subset(_u16, _u14) | ~member(skolem1(_u16, _u14), _u14) )).
% 0.67/0.87 cnf(matrix-15, plain, ( ( _u21 != _u19) | subset(_u21, _u19) )).
% 0.67/0.87 cnf(matrix-16, plain, ( ( _u21 != _u19) | subset(_u19, _u21) )).
% 0.67/0.87 cnf(matrix-17, plain, ( ~subset(_u22, _u20) | ~subset(_u20, _u22) | ( _u22 = _u20) )).
% 0.67/0.87 cnf(matrix-18, plain, ( ( union(_u24, _u23) = union(_u23, _u24)) )).
% 0.67/0.87 cnf(matrix-19, plain, ( subset(_u25, _u25) )).
% 0.67/0.87 cnf(matrix-20, plain, ( ( _u36 != _u34) | ~member(_u30, _u36) | member(_u30, _u34) )).
% 0.67/0.87 cnf(matrix-21, plain, ( ( _u36 != _u34) | ~member(_u31, _u34) | member(_u31, _u36) )).
% 0.67/0.87 cnf(matrix-22, plain, ( ( _u37 = _u35) | member(skolem2(_u37, _u35), _u37) | member(skolem3(_u37, _u35), _u35) )).
% 0.67/0.87 cnf(matrix-23, plain, ( ( _u37 = _u35) | member(skolem2(_u37, _u35), _u37) | ~member(skolem3(_u37, _u35), _u37) )).
% 0.67/0.87 cnf(matrix-24, plain, ( ( _u37 = _u35) | ~member(skolem2(_u37, _u35), _u35) | member(skolem3(_u37, _u35), _u35) )).
% 0.67/0.87 cnf(matrix-25, plain, ( ( _u37 = _u35) | ~member(skolem2(_u37, _u35), _u35) | ~member(skolem3(_u37, _u35), _u37) )).
% 0.67/0.87 cnf(matrix-26, plain, ( subset(skolem4, skolem5) )).
% 0.67/0.87 cnf(matrix-27, plain, ( ( union(skolem4, skolem5) != skolem5) )).
% 0.67/0.87
% 0.67/0.87 % Proof stack:
% 0.67/0.87 cnf(proof-stack, plain,
% 0.67/0.87 proof_stack(
% 0.67/0.87 start(27),
% 0.67/0.87 left_branch(0, 17, 2, 2),
% 0.67/0.87 left_branch(0, 14, 0, 3),
% 0.67/0.87 left_branch(0, 9, 2, 4),
% 0.67/0.87 left_branch(0, 13, 1, 5),
% 0.67/0.87 reduction(0, 1),
% 0.67/0.87 right_branch(5),
% 0.67/0.87 left_branch(0, 12, 1, 6),
% 0.67/0.87 left_branch(0, 26, 0, 7),
% 0.67/0.87 right_branch(7),
% 0.67/0.87 reduction(0, 2),
% 0.67/0.87 right_branch(6),
% 0.67/0.87 right_branch(4),
% 0.67/0.87 right_branch(3),
% 0.67/0.87 left_branch(0, 14, 0, 4),
% 0.67/0.87 left_branch(0, 11, 0, 5),
% 0.67/0.87 left_branch(0, 13, 1, 6),
% 0.67/0.87 reduction(0, 1),
% 0.67/0.87 right_branch(6),
% 0.67/0.87 right_branch(5),
% 0.67/0.87 right_branch(4),
% 0.67/0.87 right_branch(2)
% 0.67/0.87 )).
% 0.67/0.87 % SZS output end Proof for theBenchmark
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